Our NOT Gate Design, Simulations and Optimization

Design

The NOT gate (signal inverter) design we eventually used comprises of multiple double- and single-stranded species. The most important of these are NOT gate (A), output (B) and buffer (C) complexes.
There are two cases to consider: first the case where there is no input present (in digital terms, the input is 0), and second the case where there is a saturating level of input (digitally represented as a 1). We aim to convert the '0' input into a '1' output and the '1' into a '0' - the basic operation of a NOT gate. Refer to the diagram below throughout the explanation.

Case 1: No input present -> high signal
Here, the output strand (B) reversibly reacts with the NOT gate (A). The reaction is reversible because the output strand only displaces the green section on the NOT gate, but not further, meaning that the reaction could go back as well. This reversible reaction allows the output strand to react to a downstream buffer (C) and amplifier (D) to produce a high signal (a new active nucleic acid strand is released).

Case 2: Input present -> low signal
Here, the input strand and output strand both react with the NOT gate. The input strand displaces up to the pink region and the output strand displaces up to the green region. This is irreversible, as once strand displacement happens from both sides, the complex separates into two double-stranded species. There is no toehold to initiate the reverse reaction, so the output strand is "stuck". The output therefore cannot be buffered or amplified to produce a signal: no new active nucleic acid strand is released.

Diagram of our NOT gate. See the paragraph above for a more detailed description.

Optimization

The original in vitro test showed a result that did not match our simulated transfer function.

All inputs at equal concentrations, 1pmol

From the simulations, we knew that by increasing the concentration of the dynamic gate (complex A), we would get a more digital signal. We implemented this strategy by increasing the relative concentration of strand A by various amounts. Looking at the low dip in the middle concentration ranges and the rise afterwards, we determined that the cooperative hybridization was not working at the levels we were using. To test this, we raised the absolute concentration of all the parts of the NOT gate and kept the high relative concentration of complex A. This resulted in a transfer function that very nearly matched our simulation and gave us NOT gate behavior.